Integrals to know

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Calculus

Integration

University/Undergrad

Last updated 10:01 PM on 2/12/23
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16 Terms

1
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∫dx =
∫dx =
x + C
x + C
2
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∫x^r dx =
∫x^r dx =
x^(r+1) / (r+1) + C ; r =/= -1
x^(r+1) / (r+1) + C ; r =/= -1
3
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∫cos(x) dx =
∫cos(x) dx =
sin(x) + C
sin(x) + C
4
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∫sin(x) dx =
∫sin(x) dx =
\-cos(x) + C
\-cos(x) + C
5
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∫sec^2(x) dx =
∫sec^2(x) dx =
tan(x) + C
tan(x) + C
6
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∫csc^2(x) dx =
∫csc^2(x) dx =
\-cot(x) + C
\-cot(x) + C
7
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∫sec(x) tan(x) dx =
∫sec(x) tan(x) dx =
sec(x) + C
sec(x) + C
8
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∫csc(x) cot(x) dx =
∫csc(x) cot(x) dx =
\-csc(x) + C
\-csc(x) + C
9
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∫e^x dx =
∫e^x dx =
e^x + C
e^x + C
10
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∫b^x dx =
∫b^x dx =
b^x / ln(b) + C ; (0 < b, b =/= 1)
b^x / ln(b) + C ; (0 < b, b =/= 1)
11
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∫ 1/x dx =
∫ 1/x dx =
ln|x| + C
ln|x| + C
12
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∫ 1 / (1 + x^2) dx =
∫ 1 / (1 + x^2) dx =
tan^-1(x) + C
tan^-1(x) + C
13
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∫ 1 / sqrt(1 - x^2) dx =
∫ 1 / sqrt(1 - x^2) dx =
sin^-1(x) + C
sin^-1(x) + C
14
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∫ 1 / (x \* sqrt(1 - x^2)) dx =
∫ 1 / (x \* sqrt(1 - x^2)) dx =
sec^-1|x| + C
sec^-1|x| + C
15
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∫tan(x) dx =
∫tan(x) dx =
\-ln|cos(x)| + C
\-ln|cos(x)| + C
16
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∫cot(x) dx =
∫cot(x) dx =
ln|sin(x)| + C
ln|sin(x)| + C